Is it truly random or can the double down feature be part of the
strategy ? Does anyone use it or have opinions on it ?
Thanks
Using Double Down
starcast82 wrote:
Is it truly random or can the double down feature be part of the
strategy ? Does anyone use it or have opinions on it ?
IIRC one of the math gurus here did an analysis that suggested that
doubling down on the smaller winning hands will somehow help change the
variance in a way that is helpful to bankroll requirements or Risk of
Ruin; I didn't have the time to full digest it at the time, and I can't
put my hands on it to help you, but you might try doing an archive
search unless someone else comes up with it. But to answer a couple of
your questions: "Yes", it is truly random; "No", the double down
feature is not part of _play_strategy -- for example, which cards to
hold and which ones to discard -- and I don't see how it can make a
difference in your long-term ER because you should win as often as you
lose, and in the long run, average out your wins and loses on the same
size bets, too. The bottom line is to just do it if you enjoy it; there
is no real right or wrong answer. I'll let someone else tackle any
discussion of variance, although it would seems logical to me that by
addition this additional element, variance ought to go up rather than
down, and I can't see how that is helpful in reducing bankroll
requirements or RoR. But I'm open-minded enough to consider that
possibility.
Cheers.
Bill Velek
[Non-text portions of this message have been removed]
I did see a woman in casino magic in mississippi use the double up till she had the machine into a hand pay jackpot, she started with a small win, only time I ever seen anyone do this. Was on a 50 cent jacks or better.
clevgs
···
----- Original Message -----
From: Bill Velek
To: vpFREE@yahoogroups.com
Sent: Monday, February 16, 2004 2:57 PM
Subject: Re: [vpFREE] Using Double Down
starcast82 wrote:
> Is it truly random or can the double down feature be part of the
> strategy ? Does anyone use it or have opinions on it ?
IIRC one of the math gurus here did an analysis that suggested that
doubling down on the smaller winning hands will somehow help change the
variance in a way that is helpful to bankroll requirements or Risk of
Ruin; I didn't have the time to full digest it at the time, and I can't
put my hands on it to help you, but you might try doing an archive
search unless someone else comes up with it. But to answer a couple of
your questions: "Yes", it is truly random; "No", the double down
feature is not part of _play_strategy -- for example, which cards to
hold and which ones to discard -- and I don't see how it can make a
difference in your long-term ER because you should win as often as you
lose, and in the long run, average out your wins and loses on the same
size bets, too. The bottom line is to just do it if you enjoy it; there
is no real right or wrong answer. I'll let someone else tackle any
discussion of variance, although it would seems logical to me that by
addition this additional element, variance ought to go up rather than
down, and I can't see how that is helpful in reducing bankroll
requirements or RoR. But I'm open-minded enough to consider that
possibility.
Cheers.
Bill Velek
[Non-text portions of this message have been removed]
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[Non-text portions of this message have been removed]
Bill Velek wrote:
IIRC one of the math gurus here did an analysis that suggested that
doubling down on the smaller winning hands will somehow help change
the variance in a way that is helpful to bankroll requirements or
Risk of Ruin
What I believe was discussed was the fact that when a player heavily
doubles to high values they expose themselves to greater risk and it's
not prudent (although it is a fair, even money prospect).
Since some players enjoy the occasional double down, I've noted that
so long as you keep doubling to no more than 10 credit wins (and don't
redouble) that the variance of these wagers are modest and they don't
reflect undue risk relative to that of the vp play.
- Harry
As usual, if the game is negative, then using the double feature reduces
risk. This holds for all size payoffs.
···
On Monday 16 February 2004 06:04 pm, Harry Porter wrote:
Bill Velek wrote:
> IIRC one of the math gurus here did an analysis that suggested that
> doubling down on the smaller winning hands will somehow help change
> the variance in a way that is helpful to bankroll requirements or
> Risk of RuinWhat I believe was discussed was the fact that when a player heavily
doubles to high values they expose themselves to greater risk and it's
not prudent (although it is a fair, even money prospect).Since some players enjoy the occasional double down, I've noted that
so long as you keep doubling to no more than 10 credit wins (and don't
redouble) that the variance of these wagers are modest and they don't
reflect undue risk relative to that of the vp play.
Steve Jacobs:
As usual, if the game is negative, then using the double feature
reduces risk. This holds for all size payoffs.
I'll venture a question here, Steve.
Mind you, I get a little nervous in our discussions these days
whenever the word "risk" is floating about. For that matter, I start
questioning the agility of my mind once we get going 
...
Simply put, is a 9/6 Jacks player who doubles and redoubles on every
win, to jackpot or bust, playing a less risky game than the Jacks
player who never doubles?
I don't think this is what you suggesting, but it wouldn't be at all a
kick to the head if you came back and said you were 
- Harry
Steve Jacobs wrote:
snip
As usual, if the game is negative, then using the double feature reduces
risk. This holds for all size payoffs.
snip
I think that depends on whether you're going to double for all winning hands, and how many times you are going to double. For example, if you were to always double-down just one time, and ONLY one time, after each and every winning hand, your long-term ER would remain exactly the same, because while your expected frequency of ultimate wins would be one half of what are normally expected, each win would be worth twice as much. In effect, you could take a WinPoker analysis detail screen and double the paytable values while cutting the expected frequencies in half. And it is equally true that our long-tern ER will remain the same whether you are speaking about a game which is positive or negative, ... and regardless of _how_ positive or negative it is, ... and also regardless of how many consecutive times you repeatedly double-down (although I think that you would probably need to be consistent across the board to ensure that long-term ER would ultimately remain unchanged). But while long-term ER remains unchanged, the profitability of a game is affected by the time spent doubling instead of playing VP (this has already been discussed by several folks in the past). In a nut shell, when you are playing a positive expectation game, doubling-down wastes time and reduces your average hourly profits, but when you are playing a negative expectation game, doubling-down reduces the number of games you'll have time to play at an expected loss. But aside from that, let's assume that I have picked a game with a very healty positive expectation of a full percent (just for the sake of argument). What would concern me is that most folks need a Royal at close to expected frequency to recover gradual losses that have mounted since the last Royal, and its with each Royal that most folks actually realize the average profits from their hands played with positive expectation. Long dry streaks without Royals are what really seem to threaten a bankroll (and I'm using that term in the sense of total amount of money that a person can afford to lose in their lifetime), while dry streaks without Quads are what seem to exhaust session stakes. Always doubling-down once creates a situation where the length of time between Royals upon which you will actually be paid are twice as long, although those Royals are now worth twice as much. Hitting one early and successfully doubling is probably a pretty good assurance of a nice bankroll to fall back on to substantially reduce your RoR, but missing the double-down, especially if your are in a drought, is going to make your chances of survival bleak. As I said before, doubling-down is definitely a lot of fun, but it does, in my opinion, result in a combined-play that has greater volatility than the VP game by itself, and most folks consider greater volatility to mean greater risk.
Cheers.
Bill Velek
The answer might depend on the precise definition of the phrase
"to jackpot or bust". But, I suspect that is precisely what I'm
suggesting. Risk works "backwards" in negative games, compared
to what one would expect from a positive game. The critical question
is when will you stop doubling in order to cash out and go home.
Suppose you have $1000 in your pocket and you desperately need
$1100 or else Guido and The Boys will go 9 innings against your
knees with a baseball bat. The only game is 9/6 JoB with a double
feature. If you play normal max-EV strategy for 9/6 JoB, and stop
doubling whenever your total bankroll hits/exceeds the $1100 goal,
then your knees have a higher probability of going unsmashed if you
use the double feature. This assumes that the double feature is "fair"
in that it increases variance while leaving ER unchanged.
Now I'll plug that old "Equivalent Games" post. That post showed
how to model a VP game as an endless series of coin flips using
a biased coin. The amount of bias in the coin represents risk. The
double feature is mathematically equivalent to allowing the player to
use an unbiased coin for some of the flips. If the objective is to
reach a fixed target bankroll, or go bust trying, then the player who
uses a fair coin for some of the flips will have a higher probability
of reaching the goal than a player who uses the negatively biased
coin for all flips.
The same coin-flip argument can be used for favorable games. In
this case, using the double feature hurts you because it is like
using a fair coin some of the time when you could be using a coin
that is biased in your favor.
···
On Monday 16 February 2004 07:09 pm, Harry Porter wrote:
Steve Jacobs:
> As usual, if the game is negative, then using the double feature
> reduces risk. This holds for all size payoffs.I'll venture a question here, Steve.
Mind you, I get a little nervous in our discussions these days
whenever the word "risk" is floating about. For that matter, I start
questioning the agility of my mind once we get goingSimply put, is a 9/6 Jacks player who doubles and redoubles on every
win, to jackpot or bust, playing a less risky game than the Jacks
player who never doubles?I don't think this is what you suggesting, but it wouldn't be at all a
kick to the head if you came back and said you were
Steve Jacobs wrote:
snip
> As usual, if the game is negative, then using the double feature reduces
> risk. This holds for all size payoffs.snip
I think that depends on whether you're going to double for all winning
hands, and how many times you are going to double. For example, if you
were to always double-down just one time, and ONLY one time, after each
and every winning hand, your long-term ER would remain exactly the same,
because while your expected frequency of ultimate wins would be one half
of what are normally expected, each win would be worth twice as much.
True, but the question wasn't about ER, it was about risk.
In effect, you could take a WinPoker analysis detail screen and double
the paytable values while cutting the expected frequencies in half. And
it is equally true that our long-tern ER will remain the same whether
you are speaking about a game which is positive or negative, ... and
regardless of _how_ positive or negative it is, ... and also regardless
of how many consecutive times you repeatedly double-down (although I
think that you would probably need to be consistent across the board to
ensure that long-term ER would ultimately remain unchanged). But while
long-term ER remains unchanged, the profitability of a game is affected
by the time spent doubling instead of playing VP (this has already been
discussed by several folks in the past). In a nut shell, when you are
playing a positive expectation game, doubling-down wastes time and
reduces your average hourly profits, but when you are playing a negative
expectation game, doubling-down reduces the number of games you'll have
time to play at an expected loss.
OK, so think of doubling as a fair game. Now focus real hard on doubling,
so that it becomes the "main" game while the VP is just a means of wasting
time until you get another opportunity to double. By doubling often, you
minimize the time spent playing a negative game, thus reducing your risk.
But aside from that, let's assume
that I have picked a game with a very healty positive expectation of a
full percent (just for the sake of argument).
No, let's not assume that. My comment was strictly within the context
of a negative game, and does not apply to favorable situations. If the
overall game is favorable, then doubling increases the risk that you
will lose your entire bankroll before reaching your goal.
What would concern me is
that most folks need a Royal at close to expected frequency to recover
gradual losses that have mounted since the last Royal, and its with each
Royal that most folks actually realize the average profits from their
hands played with positive expectation. Long dry streaks without Royals
are what really seem to threaten a bankroll (and I'm using that term in
the sense of total amount of money that a person can afford to lose in
their lifetime), while dry streaks without Quads are what seem to
exhaust session stakes.
This is a good argument for using a min-risk playing strategy rather than
a max-EV playing strategy. The min-risk strategy increase the probability
of surviving between royals (and between quads, for that matter).
Back to doubling...
Always doubling-down once creates a situation
where the length of time between Royals upon which you will actually be
paid are twice as long, although those Royals are now worth twice as
much. Hitting one early and successfully doubling is probably a pretty
good assurance of a nice bankroll to fall back on to substantially
reduce your RoR, but missing the double-down, especially if your are in
a drought, is going to make your chances of survival bleak.
That is correct, but it doesn't contradict my statement because my
statement was clearly qualified by "...if the game is negative...".
As I said
before, doubling-down is definitely a lot of fun, but it does, in my
opinion, result in a combined-play that has greater volatility than the
VP game by itself, and most folks consider greater volatility to mean
greater risk.
Well, those folks are correct in the context of favorable games, and
incorrect in the context of unfavorable games. Volatility and risk
are not equivalent concepts. I'll grant you that this is not widely
understood, which is partly why this discussion is happening.
···
On Monday 16 February 2004 10:16 pm, Bill Velek wrote:
Let me add one other note to the ongoing discussion here. If you
choose to double on every hand (or multiple times occasionally), you
may bring some jackpots into the "over $1200" category that would not
otherwise generate a w2g. While this would not, in and of itself,
raise your taxable income. It may require you to maintain "better"
records of your wins/losses or face an audit without much chance of
winning. If you already document your wins/losses this would not be
important.
The place where I gamble quite a bit has the double feature active on
EVERY machine. It is not all that unusual to see someone waiting to
get a w2g. My wife saw a man double a RF twice on .25 machine to get
$4000. Maybe he needed $4000 to avoid getting his knees crushed
Dick
···
--- In vpFREE@yahoogroups.com, "starcast82" <starcast82@y...> wrote:
Is it truly random or can the double down feature be part of the
strategy ? Does anyone use it or have opinions on it ?Thanks
Nice analysis Steve. My personal philosophy is I will use the double down on
games which are equal to or worse than 8/5 bonus poker. The reason for this
is the fact that there are hidden costs for using the double down feature,
and to compensate - it has to be a relatively poor game.
#1 Like the "odds" bet in craps, double down is an internal bet that does
not register for points.
#2 - related to #1, playing double down slows down my game and means I have
to play longer to fulfill casino obligation time. For example, If I normally
have to play 4 hours on a machine to earn my RFB, I would have to play 5
hours with the double down feature turned on. If time is money, I better be
compensated by a real positive swing in EV - else its not worth it.
#3 - Double down increases your chance for a machine malfunction on screens
with uncalibrated touch screens. This happened to me once, Got 4 aces for
800 coin payoff, went to change coin denominations since now I can afford it
, and double up ( beat an ace please - you sucker ) came up on the screen !
Regards...Tom
···
----- Original Message -----
From: "Steve Jacobs" <jacobs@xmission.com>
To: <vpFREE@yahoogroups.com>
Sent: Tuesday, February 17, 2004 8:20 AM
Subject: Re: [vpFREE] Re: Using Double Down
On Monday 16 February 2004 07:09 pm, Harry Porter wrote:
> Steve Jacobs:
> > As usual, if the game is negative, then using the double feature
> > reduces risk. This holds for all size payoffs.
>
> I'll venture a question here, Steve.
>
> Mind you, I get a little nervous in our discussions these days
> whenever the word "risk" is floating about. For that matter, I start
> questioning the agility of my mind once we get going
>
>
> Simply put, is a 9/6 Jacks player who doubles and redoubles on every
> win, to jackpot or bust, playing a less risky game than the Jacks
> player who never doubles?
>
> I don't think this is what you suggesting, but it wouldn't be at all a
> kick to the head if you came back and said you wereThe answer might depend on the precise definition of the phrase
"to jackpot or bust". But, I suspect that is precisely what I'm
suggesting. Risk works "backwards" in negative games, compared
to what one would expect from a positive game. The critical question
is when will you stop doubling in order to cash out and go home.Suppose you have $1000 in your pocket and you desperately need
$1100 or else Guido and The Boys will go 9 innings against your
knees with a baseball bat. The only game is 9/6 JoB with a double
feature. If you play normal max-EV strategy for 9/6 JoB, and stop
doubling whenever your total bankroll hits/exceeds the $1100 goal,
then your knees have a higher probability of going unsmashed if you
use the double feature. This assumes that the double feature is "fair"
in that it increases variance while leaving ER unchanged.Now I'll plug that old "Equivalent Games" post. That post showed
how to model a VP game as an endless series of coin flips using
a biased coin. The amount of bias in the coin represents risk. The
double feature is mathematically equivalent to allowing the player to
use an unbiased coin for some of the flips. If the objective is to
reach a fixed target bankroll, or go bust trying, then the player who
uses a fair coin for some of the flips will have a higher probability
of reaching the goal than a player who uses the negatively biased
coin for all flips.The same coin-flip argument can be used for favorable games. In
this case, using the double feature hurts you because it is like
using a fair coin some of the time when you could be using a coin
that is biased in your favor.vpFREE Links:
http://www.west-point.org/users/usma1955/20228/VP/Links.htm
Yahoo! Groups Links
Steve Jacobs wrote:
Suppose you have $1000 in your pocket and you desperately need
$1100 or else ...
You frequently propose such a scenario in your discussions and it's
certainly a valid approach.
But it doesn't address the approach most players have where they're
not primarily goal oriented but will instead come back again and again
(unless cumulative losses become too large to bear). Very few appear
to have an upside threshold from which they'd walk with the money and
never darken a casino's door again.
Or perhaps I'm short selling the extent to which "targeted bankroll"
strategies come into play for the average player.
- Harry
"Harry Porter" <harry.porter@v...> wrote:
Simply put, is a 9/6 Jacks player who doubles and redoubles on every
win, to jackpot or bust, playing a less risky game than the Jacks
player who never doubles?
Many people think that craps becomes a less risky game when you place
5x odds (or whatever) on your pass line bet. Placing those odds bets
reduces the casino's edge as a percentage of your total amount bet,
so it's easy to forget that it does nothing to reduce your expected
loss in dollar terms. I've heard even mathematically savvy people
talk as if placing odds bets at craps was somehow beneficial to their
expectation.
Doubling at 9/6 Jacks is the same. It will improve your expected
return as a percentage of total amount bet (including the doubling
bets), while doing nothing to improve expectation in dollar terms.
The bet's only value is whatever excitement the player gets by
putting that money at risk (for "free"). And as with craps odds bets,
I'm sure that the casino won't give any comp credit for doubling.
Stuart (RandomStu)
sresnick2@comcast.net
http://home.comcast.net/~sresnick2/mypage.htm
rgmustain wrote:
> Is it truly random or can the double down feature be part of the
> strategy ? Does anyone use it or have opinions on it ?
>
> ThanksLet me add one other note to the ongoing discussion here. If you
choose to double on every hand (or multiple times occasionally), you
may bring some jackpots into the "over $1200" category that would not
otherwise generate a w2g. While this would not, in and of itself,
raise your taxable income. It may require you to maintain "better"
records of your wins/losses or face an audit ...
snip
Let me also add that if you are gambling in Mississippi, this WILL
result in higher STATE income taxes -- for sure. In Mississippi, you do
not pay taxes on winnings that would NOT generate a w2g, but you DO pay
taxes (and I believe it is immediately withheld) for Jackpots of
$1200.00 or more, ... and if I understand correctly, you can't get a
refund of those taxes by off-setting your gambling losses either.
Bill Velek
[Non-text portions of this message have been removed]
···
--- In vpFREE@yahoogroups.com, "starcast82" <starcast82@y...> wrote:
Stuart wrote:
Many people think that craps becomes a less risky game when you
place 5x odds (or whatever) on your pass line bet. Placing those
odds bets reduces the casino's edge as a percentage of your total
amount bet, so it's easy to forget that it does nothing to reduce
your expected loss in dollar terms ...Doubling at 9/6 Jacks is the same. It will improve your expected
return as a percentage of total amount bet (including the doubling
bets), while doing nothing to improve expectation in dollar terms.
You're on target with craps, provided that the discussion is aimed at
expected win/loss. Adding even money wagers on top of your negative
EV wager doesn't diminish the expected loss at all. (Note, however,
risk is a different matter all together.)
However, with vp it's a different situation. The time that it takes
to play out a double reduces the number of negative EV hands that can
be played in a given alloted amount of time. The double is
essentially a substitute for a hand wager, not in addition to one.
Reduce the number of negative EV plays and you reduce loss expectation
on a negative game. From this perspective, doubling is a respectable
bet on a negative game. However, I think it's prudent to restrict
doubling to risking no more than 10 or 15 credits.
- Harry
Steve Jacobs wrote:
> Steve Jacobs wrote:
>
> snip
>
> > As usual, if the game is negative, then using the double feature reduces
> > risk. This holds for all size payoffs.
>
> snip
>
> I think that depends on whether you're going to double for all winning
> hands, and how many times you are going to double. For example, if you
> were to always double-down just one time, and ONLY one time, after each
> and every winning hand, your long-term ER would remain exactly the same,
> because while your expected frequency of ultimate wins would be one half
> of what are normally expected, each win would be worth twice as much.True, but the question wasn't about ER, it was about risk.
> In effect, you could take a WinPoker analysis detail screen and double
> the paytable values while cutting the expected frequencies in half. And
> it is equally true that our long-tern ER will remain the same whether
> you are speaking about a game which is positive or negative, ... and
> regardless of _how_ positive or negative it is, ... and also regardless
> of how many consecutive times you repeatedly double-down (although I
> think that you would probably need to be consistent across the board to
> ensure that long-term ER would ultimately remain unchanged). But while
> long-term ER remains unchanged, the profitability of a game is affected
> by the time spent doubling instead of playing VP (this has already been
> discussed by several folks in the past). In a nut shell, when you are
> playing a positive expectation game, doubling-down wastes time and
> reduces your average hourly profits, but when you are playing a negative
> expectation game, doubling-down reduces the number of games you'll have
> time to play at an expected loss.OK, so think of doubling as a fair game. Now focus real hard on doubling,
so that it becomes the "main" game while the VP is just a means of wasting
time until you get another opportunity to double. By doubling often, you
minimize the time spent playing a negative game, thus reducing your risk.
We must have a different definition of risk. I'll try another example, and I believe this illustrates my point regardless of whether we are playing an extremely positive game or an extremely negative game or one that is just average -- that is all pretty much immaterial to this next example. And I don't mean to come across as ridiculous with this extreme, but you did say, after all, to think of doubling as the main game, etc. Okay, so regardless of the desirability of the game, we decide that we will always consistently double, repeatedly, and regardless of the hand (even including Royals) ... and you will repeatedly double 15 times or bust trying. In long term play, this has no effect whatsoever on ER, but I think it has EVERYTHING to do with risk. I have another post in this thread that more completely analyzes the math, but wanted to add this quick answer before people get bored to death with this. If you played that game, the odds are that you will not collect a single coin for over 72,000 hands ($90,000.00 in quarters played full-coin). Sure, when you do hit, you will receive 32,768 times whatever that hand pays, but how many people have a stake large enough to go that long without getting anything back except cash-back and bounce-back. Now that is a very extreme example, but the results are the same to a lesser degree. If you do not have a particular goal in mind, but rather just want to play as long as possible with a given bankroll, then you begin to assume larger risks relative to a given size bankroll as you decide to _consistenly_ double-down more and more. You would not need as much of a bankroll if you were going to double down only 10 consecutive times each winning hand, but you would still need more than most of us average players can swing. And for some players, I think it is fair to say that a decision to always double down 4 consecutive times on each vp win is going to add so much volatility to the game that this would be viewed as risky by many players -- especially when you've been wanting/needing a Royal, and you've just managed to quadruple it, and you still need to double-down twice more. VERY RISKY, from a stake/stability point of view ... at least in my opinion.
snip
Volatility and risk
are not equivalent concepts. I'll grant you that this is not widely
understood, which is partly why this discussion is happening.
Well, I'll go so far as to agree that volatility is not necessary a bad thing; as was pointed out awhile ago -- I think by you -- if there was no volatility, there would be no game. But I do think that, while they might not necessarily be "equivalent" concepts, it is fair to say that with sufficient volatility and a limited stake, risk does increase ... as I think I ample illustrated, above.
Bill Velek
···
On Monday 16 February 2004 10:16 pm, Bill Velek wrote:
Steve Jacobs wrote:
> Steve Jacobs:
> > As usual, if the game is negative, then using the double feature
> > reduces risk. This holds for all size payoffs.
>
> I'll venture a question here, Steve.
>
> Mind you, I get a little nervous in our discussions these days
> whenever the word "risk" is floating about. For that matter, I start
> questioning the agility of my mind once we get going
>
> Simply put, is a 9/6 Jacks player who doubles and redoubles on every
> win, to jackpot or bust, playing a less risky game than the Jacks
> player who never doubles?
>
> I don't think this is what you suggesting, but it wouldn't be at all a
> kick to the head if you came back and said you wereThe answer might depend on the precise definition of the phrase
"to jackpot or bust". But, I suspect that is precisely what I'm
suggesting. Risk works "backwards" in negative games, compared
to what one would expect from a positive game. The critical question
is when will you stop doubling in order to cash out and go home.Suppose you have $1000 in your pocket and you desperately need
$1100 or else Guido and The Boys will go 9 innings against your
knees with a baseball bat. The only game is 9/6 JoB with a double
feature. If you play normal max-EV strategy for 9/6 JoB, and stop
doubling whenever your total bankroll hits/exceeds the $1100 goal,
then your knees have a higher probability of going unsmashed if you
use the double feature. This assumes that the double feature is "fair"
in that it increases variance while leaving ER unchanged.
Well, not to quibble, but technically I think it would be incorrect to double if it will cause you to exceed goal, as I explain further, below. But subject to that -- and to a very small percentage of exceptions based upon relative stake/goal sizes -- I'm confident that what you have said is true so long as we have a particular goal.
I'll start with what I think are likely exceptions. I don't know what the curve of a graph would look like, but at some point with a small enough stake -- relative to your goal -- you do cross the line (which I mention only academically for the sake of discussion, because such extremes have little practical application). For instance, JoB-9/6 has approximately a 45% winning-game rate. If your session stake is only a single bet, then out of the mere 45% of the time that a normal player would survive the first vp bet, a player who then doubles has only half that chance of surviving to bet again. If a person has only a 2 bet stake, it would seem to me that a doubler also has a worse chance of survival; 55% will lose their first bet on vp before ever reaching the doubling option; of the 45% who win their first bet on vp, only 22.5% will win the doubling, although some will now have much more than their original 2 bet stake. But 77.5% are now down to a single bet remaining, and if we use the same math, 77.5% of them will also lose their second bet, so after 2 bets, over 60% will be busted without ANY hope of saving their knees. Now, in comparison to the regular win-loss rates for the same game, with a 55% chance of losing each vp game, after two bets, only 30% will be busted without any hope of saving their knees. I used a VERY small bankroll just to make it easy for folks to see what I mean. Now, I don't know where the lines cross on a graph, and I'm not going to go through that much work for this, but at some point, and no doubt VERY quickly, as soon as your stake is increased to a certain point, then it would immediately become advantageous to switch to doubling all winning hands for as long as your stake does not dip below that level.
Now before going on to my other theory that you would never double if it will put you beyond your goal, lets take another example of a more realistic figure. Let's say that you owe Guido $1500.00 and you have a modest but perhaps somewhat realistic $65.00 in your pocket (in other words, you have a 52 bet stake on a JoB quarter machine, and you need to build it into a 1200 bet stake). I had arbitrarily started with an even 50-bet stake ($62.50) but discovered that I could not enter a fraction of a dollar in Jeff Lotspiech's "Gambler Ruin Calculator", so I bumped it up to an even $65.00 and then also ran it for an even $60.00 (48 bets). So for this discussion I will speak in terms of 'betting units' rather than dollars or coins, because it's easier, and when I speaking about 1, 2, 3, etc., "wins", I am still talking about full-coin such that 1 win really means 5 quarters. On each winning-bet you proposed doubling until you either bust or your stake exceeds 1000, so that's what we'll do. On your first bet, you need to win 1151 to meet you goal, with the following expected results:
54.543% of the time you lose the VP bet and never get a chance to double
21.459% of the time you win 1 and must then double-down 11 times with chances of winning = 1/2048 x the 21.459% = 1/2048*.21459= 0.0001047802734375
12.928% -- you win 2 and d-d 10 times = 1/1024*.12928= 0.00012625
7.445% -- you win 3 and d-d 9 times = 1/512*.07445= 0.00014541015625
1.123% -- win 4 d-d 9 times = 1/512*.01123= 0.00002193359375
1.101% -- win 6 d-d 8 times = 1/256*.01101= 0.0000430078125
1.151% -- win 9 d-d 8 times = 1/256*.01151= 0.0000449609375
0.236% -- win 25 d-d 6 times = 1/64*.00236= 0.000036875
0.011% -- win 50 d-d 5 times = 1/32*.00011= 0.0000034375
0.002% -- win 800 d-d 1 time = 1/2*.00002= 0.00001
Your Total odds of meeting your goal on the first bet is 0.0005366552734375
Your odds of failing and having to bet further is 0.9994633447265625
Now, your 'stake' at the end of each "try" will NEVER be bigger than it is when you start, or else you will have already met your goal and stopped. This means that your stake is constantly diminishing as you repeat your attempts, and the amount that you need to meet your goal constantly increases. The result is that for each bet (assuming the same size gap between stake and goal), your odds are NEVER going to be better than the above, although for this particular beginning stake and goal, they won't get any worse, either.
With a stake of 52 bets and odds of failing of 0.9994633447265625 each time, your chances of ultimately going bust is 0.9724724189488650115689794580225
or a chance of making it of only 0.027527581051134988431020541977496 = 2.75% This compares to a success rate of 3.10% when using what I presume is max-ER strategy and NEVER doubling. This can be confirmed on Jeff Lotspiech's Calculator at http://www.lotspiech.com/GamblersRuin.html -- which I presume is max-ER -- but you need to be patient since Jeff's calculator needs to run somewhat over 100K hands to reach at least 3.1% 'retired', and it was still at that level about 250,000 hands. I would also assume that that figure could also be improved slightly using your own min-risk strategy, Steve.
By the way, the figures when starting with a 48-bet stake ($60.00) are as follows: using 'doubling', your chances of success drop from 2.75% to only 2.54%, and with NO doubling, your chances drop from 3.10% to 2.80%, which is still better than the doubling success-rate.
I do agree with a comment that Harry Porter recently made that this probably doesn't matter as much to folks who are planning to stop playing when they hit a particular goal; oh, they might stop after a big win -- for that particular trip -- but if they even return to the casino again, then in keeping with the concept of just a single session in life, doubling during parts of their session isn't expected to really make any difference in the long-run. If they like it, then they should do it, keeping in mind that they are risking greater tax liability and possibly reduced comps for a given amount of time playing.
HOWEVER, all of that having been said, your point is well-taken Steve, and I think you are correct that in the vast marjority of instances where you have a goal that must be met -- especially with 'Guido and The Boys' breathing down your back -- it is no doubt best to add doubling. But I do think that one should use a blend of not-doubling when their stake is about to bottom-out, but doubling whenever their stake is 'safe' ... but not when doubling will exceed the goal. This last point can be seen quite easily when you are in the situation of hitting a Royal to bring you within a few dollars of your goal; it would clearly be insane to double at that point. Instead, you take your winnings and resuming doubling on the following hands.
Cheers.
Bill Velek
···
On Monday 16 February 2004 07:09 pm, Harry Porter wrote:
Steve Jacobs wrote:
> Suppose you have $1000 in your pocket and you desperately need
> $1100 or else ...You frequently propose such a scenario in your discussions and it's
certainly a valid approach.But it doesn't address the approach most players have where they're
not primarily goal oriented but will instead come back again and again
(unless cumulative losses become too large to bear). Very few appear
to have an upside threshold from which they'd walk with the money and
never darken a casino's door again.
That approach, combined with negative games, spells certain doom.
Using the double feature will surely delay that doom, but not prevent
it. I would suggest that the delay of doom is a manifestation of reduced
risk. Perhaps not useful, but those who choose to play negative games
endlessly cannot be helped in very meaningful ways.
In the context of favorable games, one can always use the present
goal as a "stepping stone" toward higher goals. This amounts to using
pure dollars as the benchmark for progress, without accounting for
(or even worrying about) the number of hands played. In favorable
games, the min-risk strategy can be played endlessly, and will move
from one min-risk stepping stone to the next, in sequence, all the
while minimizing the risk of going broke before reaching the next
stepping stone.
In contrast, if you employ a max-EV strategy, you will experience
a greater probability of going broke before reaching any chosen
stepping stone. This may be worth thinking about. If you start
with a small bankroll and play to play far into the future, and
you compute your EV for 1 million hands of play, the resulting
EV will be based on a large number of "paths" that would take
the bankroll negative, possibly very negative, before reaching
the 1 million hand mark. Now, unless you allow yourself infinite
credit, those path shouldn't really be counted as part of your
average outcome. Thus, max-EV is perhaps somewhat bogus,
because it assumes unlimited credit. In contrast, min-risk is
ever mindful of the finite nature of your bankroll, and so risk-
based computations/predictions are in a sense more exact
than the corresponding EV based computations/predictions.
In other words, some of the "value" of EV is inherently
unattainable for a player who starts with a bankroll that is
truly finite.
Or perhaps I'm short selling the extent to which "targeted bankroll"
strategies come into play for the average player.
I don't know. But, I think similar objections can be raised in regard
to _any_ means of measuring "progress". EV measure progress in
terms of dollars per game played, but do you know _anyone_ who
actually keeps track of the exact number of games played in order
to assess how well they are doing? The more I study alternate
strategies, the more I realize that EV just isn't that great of a way
to measure progress. I've always said "EV isn't everything" but
lately I'm leaning more and more toward "EV isn't much of anything".
(Blasphemy!)
The nice thing about framing things in terms of a fixed goal is
that it makes clear exactly what the player is trying to accomplish.
The objective then becomes maximization of the expected value
of the player's final bankroll, which is equivalent to maximizing
the probability of reaching the goal, which is equivalent to
minimizing risk. I still find it rather striking that in this scenario,
the way to get the most average dollars overall is _not_ to play
for the most average dollars on each individual wager.
···
On Tuesday 17 February 2004 09:30 am, Harry Porter wrote:
"Harry Porter" <harry.porter@v...> wrote:
> Simply put, is a 9/6 Jacks player who doubles and redoubles on every
> win, to jackpot or bust, playing a less risky game than the Jacks
> player who never doubles?Many people think that craps becomes a less risky game when you place
5x odds (or whatever) on your pass line bet. Placing those odds bets
reduces the casino's edge as a percentage of your total amount bet,
so it's easy to forget that it does nothing to reduce your expected
loss in dollar terms. I've heard even mathematically savvy people
talk as if placing odds bets at craps was somehow beneficial to their
expectation.
It depends on how you frame your definition of "expectation." But,
setting that aside, taking odds at craps does reduce risk.
Doubling at 9/6 Jacks is the same. It will improve your expected
return as a percentage of total amount bet (including the doubling
bets), while doing nothing to improve expectation in dollar terms.
The bet's only value is whatever excitement the player gets by
putting that money at risk (for "free"). And as with craps odds bets,
I'm sure that the casino won't give any comp credit for doubling.
There is more value here than excitement. If the player has a fixed
target, reducing risk is the same as increasing the probability of
reaching the target. Then by averaging over all possible outcomes,
the player with lower risk will have a greater expected value for
final bankroll, by virtue of reaching the target with greater
probability. The word "risk" is really a code-word for "probability
of failure".
Reducing risk translates to a real impact on _overall_ dollar outcome,
even though the EV (based on a single wager) is unchanged. So,
when you say "doing nothing to improve expectation in dollar terms"
it is true if you are talking about dollar terms of a single wager, but
false if you are talking dollar terms based on the probability of
reaching a target bankroll and quitting.
People tend to think of EV as a means of measuring "dollar outcome"
while risk is some nebulous thing that measures something else,
but really they are two different ways of measuring "dollar outcome".
EV measures in terms of dollars per game played, while risk measures
in terms of dollars per "target reached". Clearly they are different
measures, but both are ways to assess player performance.
···
On Tuesday 17 February 2004 12:24 pm, Stuart wrote:
Stuart wrote:
> Many people think that craps becomes a less risky game when you
> place 5x odds (or whatever) on your pass line bet. Placing those
> odds bets reduces the casino's edge as a percentage of your total
> amount bet, so it's easy to forget that it does nothing to reduce
> your expected loss in dollar terms ...
>
> Doubling at 9/6 Jacks is the same. It will improve your expected
> return as a percentage of total amount bet (including the doubling
> bets), while doing nothing to improve expectation in dollar terms.You're on target with craps, provided that the discussion is aimed at
expected win/loss. Adding even money wagers on top of your negative
EV wager doesn't diminish the expected loss at all. (Note, however,
risk is a different matter all together.)However, with vp it's a different situation. The time that it takes
to play out a double reduces the number of negative EV hands that can
be played in a given alloted amount of time. The double is
essentially a substitute for a hand wager, not in addition to one.
VP is different in the sense that odds bets increase the win/loss without
changing the probabilities of win/lose, while doubling changes the
probability of win/loss and increases the size of wins without increasing
the size of losses. Both have the effect of altering risk while leaving
EV unchanged. I suspect that doubling on VP wagers is more effective
at reducing risk than taking odds at the craps table.
Roulette is a wonderful game for studying risk. All plays (modulo the
goofy 5-spot play on double-zero wheels) have the same EV, so the
real difference between the roulette wagers is the risk. Even money
bets have a risk parameter of 1.11111... while betting on a single
number reduces the risk to 1.003065.
Reduce the number of negative EV plays and you reduce loss expectation
on a negative game. From this perspective, doubling is a respectable
bet on a negative game. However, I think it's prudent to restrict
doubling to risking no more than 10 or 15 credits.
Why is this prudent? Bill pointed out that doubling may not be correct
if it causes you to exceed your goal, and there is some mathematical
justification for that claim (if doubling a large payoff would only exceed
the goal by a small amount, then doubling is still lower risk). From a risk
perspective, foregoing a double harms the player much like deviating
from optimal playing strategy. Here it is a deviation from the optimal
wagering strategy, but the concept remains the same. The effect of not
doubling is to make your credits last longer, at the expense of increasing
the certainty that you will lose. It is kind of like taking a little extra
time to pound a nail into your own coffin, rather than perform an action
that will increase the probability that you will escape from the coffin.
It seems to me that you might be thinking about the scenario where
the player always keeps doubling until inevitably losing each wager.
This scenario is equivalent to attempting to extract a long-term
win from a negative game, which is mathematically impossible.
It does raise an interesting question though -- is it more important
to double small payoffs, or large payoffs? I'll have to look into
this some more...
···
On Tuesday 17 February 2004 01:53 pm, Harry Porter wrote: